Definition 2.4 (see [1]}) For any objects \(A, B\)  of \(\mathcal {C}\) , choose a \(\xi \) -projective resolution \({\mathbf {P}[r]& A}\)  of \(A\) . For any integer \(n\geqslant 0\) , the \(\xi \) -cohomology groups are defined as
\(\xi {\rm xt}_{\mathcal {P}}^n(A,B)=H^n(\mathcal {C}(\mathbf {P},B))\) .

